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Parts I–II: Review and revise your individualproject fro

Parts I–II: Review and revise your individualproject fro

Parts I–II: Review and revise your individualproject from last week. You must include parts I and II from IndividualProject #4 as they will be graded again. Then, add the followingresponses to your document:Part III: Regression and CorrelationBased on what you have learned from your research on regressionanalysis and correlation, answer the following questions about the BodyFat Versus Weight data set:When performing a regression analysis, it is important to firstidentify your independent/predictor variable versus yourdependent/response variable, or simply put, your x versus y variables. How do you decide which variable is your predictor variable and which is your response variable? Basedon the Body Fat Versus Weight data set, which variable is the predictorvariable? Which variable is the response variable? Explain.Using Excel, construct a scatter plot of your data.Usingthe graph and intuition, determine whether there is a positivecorrelation, a negative correlation, or no correlation. How did you cometo this conclusion?Calculate the correlation coefficient, r,and verify your conclusion with your scatter plot. What does thecorrelation coefficient determine? Discuss the strength of thecorrelation coefficient calculated, and if the correlation is positiveor negative.Add a regression line to your scatter plot, and obtain the regression equation.Does the line appear to be a good fit for the data? Why or why not? Regression equations help you make predictions. Using yourregression equation, discuss what the slope means, and determine thepredicted value of body fat x = 0. Interpret the meaning of thisequation. Part IV: Putting it TogetherYour analysis is now complete, and you are ready to report yourfindings to your boss. In one paragraph, summarize your results byexplaining your findings from the statistical measures, hypothesis test,and regression analysis of body fat and weight for the 252 menattending Silver’s GymINFO That MAY NEEDEDPart IThe mean, median, range, andstandard deviation for the Body Fat and Weight data are computed in thefollowing TableMeasureBODYFATWEIGHTMean18.94178.92Median19.00176.50Range45.10244.65Standard Deviation7.7529.39Mean and medianare two commonly used measures of central tendency.  Mean is the sum of observa­tions divided bythe total number of observations. Median is the midpoint of the values afterall observations have been ordered from the smallest to the largest. Theaverage body fat and weight of men who attend the gym are 18.94 and 178.92respectively. The median values of body fat and weight are 19.0 and 176.5respectively. The mean and median values of body fat and weight are close.Range and Standard deviation are measures of dispersion. They show thevariability in the data. Range is the difference between the largest andsmallest values in a data set. Standard deviation is the square root of thearithmetic mean of the squared deviations from the mean. The purpose of mean and median is to pinpoint the center of aset of observations. Mean and median are useful measure for comparing two ormore populations.The mean is not representative of data with extreme values.The median is a useful measure when we encounter data with an extreme value.In this data set, the mean maybe more useful than the median, because of the relatively large sample sizewhich will not be as heavilyimpacted by statistical outliers.A direct comparison of two setsof data based only on two measures of location such as the mean and the mediancan be misleading since an average does not tell us anything about the spreadof the data. In such situation we use the measures of dispersion range orstandard deviation.Part II Let μ denote the meanbody fat in men attending Silver’s Gym. The null andalternative hypotheses areHo:μ = 20Ha: μ ≠ 20Since the alternativehypothesis contains the not-equal-to symbol, the test is two-tailed test. The significance level ofthe test is given to be α = 0.05.Since the sample size (n = 252 > 30) is large, we can usethe z–test for testing the hypothesis.The critical values at α =0.05 are –z0 = -1.96 and z0 = 1.96. Therefore, therejection regions are to the left of –z0= -1.96 and to the right of z0= 1.96. The standardized teststatistic is  z = (xbar –μ)/(σ/√n)Since the sample size n > 30, we can use σ ≈ s, the samplestandard deviation.For the body fat data, n = 252, xbar = 18.94 and s = 7.75.Therefore, z = (18.94 – 20)/(7.75/√252) = -2.17The decision rule is:Reject Ho if z < -1.96 or z > 1.96.Since z < -1.96 it is in the rejection region and we reject the nullhypothesis Ho.Thus, there is sufficientevidence to reject the claim that the mean body fat inmen attending Silver’s Gym is 20%.Supplement:IDNOBODYFATWEIGHT112.6154.25Description:The dataset provided hereis based on a sample of 252 men. 26.9173.25Their body fat andweights were recorded. 324.6154.00 410.9184.75Statement:The doctors office claimsthat the mean body fat in men is 20%. 527.8184.25 620.6210.25Source:http://www2.stetson.edu/~jrasp/data.htm 719.0181.00 812.8176.00 95.1191.00 1012.0198.25 117.5186.25 128.5216.00 1320.5180.50 1420.8205.25 1521.7187.75 1620.5162.75          1728.1195.75          1822.4209.25          1916.1183.75          2016.5211.75          2119.0179.00          2215.3200.50          2315.7140.25          2417.6148.75          2514.2151.25          264.6159.25          278.5131.50          2822.4148.00          294.7133.25          309.4160.75          3112.3182.00          326.5160.25          3313.4168.00          3420.9218.50          3531.1247.25          3638.2191.75          3723.6202.25          3827.5196.75          3933.8363.15          4031.3203.00          4133.1262.75          4231.7205.00          4330.4217.00          4430.8212.00          458.4125.25          4614.1164.25          4711.2133.50          486.4148.50          4913.4135.75          505.0127.50          5110.7158.25          527.4139.25          538.7137.25          547.1152.75          554.9136.25          5622.2198.00          5720.1181.50          5827.1201.25          5930.4202.50          6024.0179.75          6125.4216.00          6228.8178.75          6329.6193.25          6425.1178.00          6531.0205.50          6628.9183.50          6721.1151.50          6814.0154.75          697.1155.25          7013.2156.75          7123.7167.50          729.4146.75          739.1160.75          7413.7125.00          7512.0143.00          7618.3148.25          779.2162.50          7821.7177.75          7921.1161.25          8018.6171.25          8130.2163.75          8226.0150.25          8318.2190.25          8426.2170.75          8526.1168.00          8625.8167.00          8715.0157.75          8822.6160.00          898.8176.75          9014.3176.00          9120.2177.00          9218.1179.75          939.2165.25          9424.2192.50          959.6184.25          9617.3224.50          9710.1188.75          9811.1162.50          9917.7156.50          10021.7197.00          10120.8198.50          10220.1173.75          10319.8172.75          10421.9196.75          10524.7177.00          10617.8165.50          10719.1200.25          10818.2203.25          10917.2194.00          11021.0168.50          11119.5170.75          11227.1183.25          11321.6178.25          11420.9163.00          11525.9175.25          11616.7158.00          11719.8177.25          11814.1179.00          11925.1191.00          12017.9187.50          12127.0206.50          12224.6185.25          12314.8160.25          12416.0151.50          12514.0161.00          12617.4167.00          12726.4177.50          12817.4152.25          12920.4192.25          13015.0165.25          13118.0171.75          13222.2171.25          13323.1197.00          13425.3157.00          13523.8168.25          13626.3186.00          13721.4166.75          13828.4187.75          13921.8168.25          14020.1212.75          14124.3176.75          14218.1173.25          14322.7167.00          1449.9159.75          14510.8188.15          14614.4156.00          14719.0208.50          14828.6206.50          1496.1143.75          15024.5223.00          1519.9152.25          15219.1241.75          15310.6146.00          15416.5156.75          15520.5200.25          15617.2171.50          15730.1205.75          15810.5182.50          15912.8136.50          16022.0177.25          1619.9151.25          16214.8196.00          16313.3184.25          16415.2140.00          16526.5218.75          16619.0217.00          16721.4166.25          16820.0224.75          16934.7228.25          17016.5172.75          1714.1152.25          1721.9125.75          17320.2177.25          17416.8176.25          17524.6226.75          17610.4145.25          17713.4151.00          17828.8241.25          17922.0187.25          18016.8234.75           18125.8219.25          1820.0118.50          18311.9145.75          18412.4159.25          18517.4170.50          1869.2167.50          18723.0232.75          18820.1210.50          18920.2202.25          19023.8185.00          19111.8153.00          19236.5244.25          19316.0193.50          19424.0224.75          19522.3162.75          19624.8180.00          19721.5156.25          19817.6168.00          1997.3167.25          20022.6170.75          20112.5178.25          20221.7150.00          20327.7200.50          2046.8184.00          20533.4223.00          20616.6208.75          20731.7166.00          20831.5195.00          20910.1160.50          21011.3159.75          2117.8140.50          21226.4216.25          21319.3168.25          21418.5194.75          21519.3172.75          21645.1219.00          21713.8149.25          2188.2154.50          21923.9199.25          22015.1154.50          22112.7153.25          22225.3230.00          22311.9161.75          2246.1142.25          22511.3179.75          22612.8126.50          22714.9169.50          22824.5198.50          22915.0174.50          23016.9167.75          23111.1147.75          23216.1182.25          23315.5175.50          23425.9161.75          23525.5157.75          23618.4168.75          23724.0191.50          23826.4219.15          23912.7155.25          24028.8189.75          24117.0127.50          24233.6224.50          24329.3234.25          24431.4227.75          24528.1199.50          24615.3155.50          24729.1215.50          24811.5134.25          24932.3201.00          25028.3186.75          25125.3190.75          25230.7207.50           – mongo0517 days ago

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NB

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